This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Seismic inversion is a process of extracting subsurface information from the data measured at the surface of the earth acquired during a seismic survey. In a typical seismic survey, seismic waves are generated by a source positioned at desired locations. As the source generated wave propagates through the subsurface, some of the energy reflects from subsurface interfaces and travels back to the receiver locations where it is recorded. The seismic waves that have been reflected once are called primary reflections. In contrast, multiple reflections are the seismic waves that have been reflected more than once before being recorded by the receivers. Multiples can be characterized as (i) free-surface related multiples, and (ii) internal multiples. The former are those multiples that are reflected from the top surface and will disappear if that surface becomes non-reflecting.
FIG. 1 provides an example of inter-bed multiples. Source 107 emits two seismic waves 100 and 101. FIG. 1 depicts how waves 100 and 101 can reflect from reflectors 102, 103, and 104 as they travel to receiver 106. FIG. 1 assumes free surface 105.
FIG. 2 provides an example of free surface multiples. Source 207 emits two seismic waves 200 and 201, which are received by receivers 206. FIG. 2 depicts how waves 200 and 201 reflect off of reflectors 202, 203, and 204, and free surface 205.
Most seismic imaging methods uses only primary data and treat multiple data as noise (i.e., unwanted features in the data) that needs to be removed during conventional data processing. There are several methods for multiple suppression methods in industry. For example, suppression methods include surface-related multiple elimination (SRME), shallow water demultiple (SWD), model-based water-layer demultiple (MWD), and predictive deconvolution. Those of ordinary skill in the art are familiar with these suppression methods, and further discussion is not needed. However, all of the methods struggle with multiple elimination if the multiple and primary reflections overlap in the recorded seismic data. Furthermore, inadequate application of multiple suppression methods may result in damage to the primary data, rendering it unusable for inversion. All of these methods suffer as multiples and primaries are difficult to separate, data processing can damage primary data, and image quality can be degraded.
Full waveform inversion (FWI) is a seismic imaging method which can utilize the full seismic record including events that are treated as “noise” by standard inversion algorithms. FWI creates a model which, when used to drive numerical simulation, optimally matches the measured data. The numerical simulations can generate data with or without free-surface-related multiples depending on the free-surface boundary condition. The free-surface boundary condition generates data with surface-related multiples, while the non-reflecting (absorbing) boundary condition allows for generation of data free from surface-related multiples. Internal multiples are present in both types of surface boundary conditions.
The crux of any FWI algorithm can be described as follows: using a starting subsurface physical property model, synthetic seismic data are generated, i.e. modeled or simulated, by solving the wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The term velocity model or physical property model as used herein refers to an array of numbers, typically a 3-D array, where each number, which may be called a model parameter, is a value of velocity or another physical property in a cell, where a subsurface region has been conceptually divided into discrete cells for computational purposes. The synthetic seismic data are compared with the field seismic data and using the difference between the two, an error or objective function is calculated. Using the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to generate a new objective function. This process is repeated until the objective function is satisfactorily minimized and the final subsurface model is generated. A global or local optimization method is used to minimize the objective function and to update the subsurface model.
Numerical simulation can generate data with or without free surface multiples depending on the free surface boundary condition imposed on the top of the subsurface model. The free surface boundary condition yields data with surface-related multiples, while the transparent (absorbing) boundary condition allows for generation of multiple-free data. These two modes of numerical modeling lead to two standard approaches in FWI.
In a first approach, FWI can utilize input seismic data having undergone some kind of multiple suppression procedure and uses an absorbing boundary condition to model the synthetic data. This approach only suppresses free surface multiples and its success hinges on the multiple suppression techniques. In a second FWI approach, the data still contain surface-related multiples which have to be modeled by using a free-surface boundary condition.
The second approach saves both time and resources required by conventional multiple processing methods. Furthermore, it ensures that integrity of the data is not compromised. The drawback of the second approach is that it requires an accurate modeling of surface-related multiples. This is extremely difficult for several reasons: (i) residuals in the multiple data are very sensitive to the error in the reflectivity of the primary reflector (e.g., the water bottom reflectivity for the surface related multiple) and (ii) field data might include reflections that cannot be modeled by the given synthetic numerical model (such as elastic affects, attenuation and anisotropy). The most crucial impediment is that even a small data mismatch between the measured and simulated multiples can create undesired multiple artifacts in the image.
U.S. Pat. No. 7,974,824, the entire contents of which are hereby incorporated by reference, describes the seismic inversion of data containing surface-related multiples. Instead of pre-processing seismic data to remove surface-related multiples, a seismic waveform inversion process enables comparison of simulated seismic data containing surface-related multiples with observed seismic data also containing surface-related multiples. Based on this comparing, a model of a subterranean structure can be iteratively updated.
Zhang and Schuster (2013) describes a method where least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. Zhang D. and Schuster G., “Least-squares reverse time migration of multiples,” Geophysics, Vol. 79, S11-S21, 2013, the entire contents of which are hereby incorporated by reference.